There are several ways to run TiddlyWeb under Apache:

• run it as a CGI (not recommended, unless you have no alternatives)
  
• run it under mod_python (not recommended)
  
• run it under mod_wsgi (recommended)
  
• run it under Fast CGI
  
• use Apache as a proxy (experimental)
  
  

While TiddlyWeb should work with 1.3.x versions of Apache, it is probably best to use 2.x versions.